Subtle effects influencing the results of orbit determination have to be taken into consideration when recomputing the cometary orbits for the Catalogue. It is very important to apply the numerical integration method, taking into account the specific conditions of the comet's motion, which almost eliminates a cumulation of numerical errors of integration. In this point of view the recurrent power series integration is adapted for cometary orbital computations. The optimal value of step-size of integration according to the required accuracy is calculated at every integration step. The method gives excellent results for “normal” comets as well as in the cases of close approaches of a comet to the Sun and to the planets.